Analysis of the symmetry of a stressed medium using nonlinear elasticity

Velocity variations caused by subsurface stress changes play an important role in monitoring compacting reservoirs and in several other applications of seismic methods. A general way to describe stress- or strain-induced velocity fields is by employing the theory of nonlinear elasticity, which operates with third-order elastic (TOE) tensors. These sixth-rank strain-sensitivity tensors, however, are difficult to manipulate because of the large number of terms involved in the algebraic operations. Thus, even evaluation of the anisotropic symmetry of a medium under stress/strain proves to be a challenging task. We employ a matrix representation of TOE tensors that allows computation of strain-related stiffness perturbations from a linear combination of 6×6 matrices scaled by the components of the strain tensor. In addition to streamlining the numerical algorithm, this approach helps to predict strain-induced symmetry using relatively straightforward algebraic considerations. For example, our analysis shows that a transversely isotropic (TI) medium acquires orthorhombic symmetry if one of the principal directions of the strain tensor is aligned with the symmetry axis. Otherwise, the strained TI medium can become monoclinic or even triclinic.